They might not represent the kind of records Patriots fans have become accustomed to — if anything, it’s a sign of the team’s struggles on offense — but for a punter, it’s what he’s paid to do. Allen’s kicks went for a 46.7-yard average, with four downed inside the Jets’ 20-yard-line. His long was 60.

Not counting the final possession, when Tom Brady took a knee to end the game, every Patriots series in the second half ended the same way: With an Allen punt.

“I’m just focused on doing my job and doing it to the best of my ability,” Allen said. “If I’m called upon that many times, then I need to step in there and do well for the team.”

Allen said the referees did a good job keeping the game balls dry during the second-half soaking, but credited long snapper Danny Aiken, who gave Allen solid snaps the entire night.

Deal or no deal?

A NFL Network report before Thursday’s game said that Bill Belichick has agreed with the Patriots to an extension of his contract, which was set to expire after the 2013 season.

Down on situation

Perhaps there was no greater indicator of the Patriots’ struggles on offense Thursday than in their third-down performance. They were just 4 for 18 converting third downs, their worst performance, percentage-wise, since going 2 for 15 against the 49ers last season.

Ten of the 14 third-down failures came when the Patriots had 8 yards or fewer to go for a first down. Twice they couldn’t convert on third and 1, and two more times they failed to move the chains on third and 3.

“It’s never good to be in long yardage. But they weren’t all long-yardage situations,” Belichick said. “Offensively, we can improve in every area: running the ball, passing the ball, red area, third down, making the big plays in the opportunities that we had.”

A beauty to him

Elise Amendola/Associated Press

Alfonzo Dennard’s fourth-quarter interception Thursday was his fourth in 12 career games.

Alfonzo Dennard had his first interception of the season Thursday and fourth of his career, picking off Geno Smith in the fourth quarter. He was fine talking about that . . . to a point.

“It felt good to get an interception, but the win is more important than anything else,” Dennard said. “There’s no such thing as an ugly win. If the offense isn’t putting it on, then the defense has to put it on, and if the defense isn’t putting it on, then the offense does. It’s a team thing.”

One topic Dennard had no interest in discussing was his upcoming court date in Lincoln, Neb. Dennard is scheduled to appear before a judge on Monday for a probation violation hearing.

“I’m just enjoying this win right now, I’m not going to talk about that,” Dennard said, when asked if he’ll need to travel to Nebraska for Monday’s scheduled hearing.

Movin’ on up

Brady moved past former teammate Drew Bledsoe on the NFL’s career completions chart. With 3,846, Brady is now seventh on the list; Bledsoe had 3,839. Up next is Warren Moon, who had 3,988
. . . The Patriots have won 12 straight games over AFC East opponents. They won the last four games against division rivals in the 2011 season, went 6-0 last year, and have two victories this season . . . Buffalo linebacker Arthur Moats was fined $7,875 for his facemask of Julian Edelman in Sunday’s game, according to the league. No Patriots drew first-game fines . . . The Patriots made a minor practice squad roster shuffle involving offensive linemen, re-signing Josh Kline and releasing R.J. Dill . . . Thursday’s game drew a combined household rating of 34.2 from the NFL Network’s broadcast and local coverage from WCVB and WMUR. That’s an 11 percent increase from the Week 1 win over the Bills (30.8 on WBZ).